Voltage Regulators Placement in Unbalanced Radial Distribution Systems for Loss Minimization Using Particle Swarm Optimization

ISSN 2349-7815
International Journal of Recent Research in Electrical and Electronics Engineering (IJRREEE)
Vol. 1, Issue 3, pp: (11-22), Month: October - December 2014, Available at: www.paperpublications.org
Page | 11
Paper Publications
Voltage Regulators Placement in Unbalanced Radial Distribution Systems for Loss Minimization Using Particle Swarm Optimization
Namrata Sahu
ME Control System, Department of Electrical Engineering, Jabalpur Engineering College, Jabalpur, INDIA
Abstract: The Automatic Voltage Regulators (AVRs) help to reduce energy loss and improve the power quality of electric utilities. This paper presents selection of optimal location and tap setting for voltage regulators in Unbalanced Radial Distribution Systems (URDS). Power loss index (PLI) is used for the selection of optimal location of voltage regulators which will first found at each branch except source bus and the bus that has the highest power loss index are picked as the best location for the voltage regulators placement. Particle swarm optimization (PSO), is used for selecting the tap position of voltage regulator in an unbalanced radial distribution system. This algorithm makes the initial selection and tap position setting of the voltage regulators to minimize power losses and provide a good voltage profile along the distribution network and then reduce the total cost to obtain the maximum net savings. The effectiveness of the proposed method is illustrated on a test system of IEEE 33 bus unbalanced radial distribution systems.
Keywords: Unbalanced Radial Distribution Systems (URDS), Load Flow, Power loss index(PLI),Particle swarm optimization(PSO), Voltage Regulator placement, Loss minimization, cost saving.
I. INTRODUCTION
Distribution systems are the networks that transport the electrical energy from bulk substation to many services or loads. Losses in a distribution system are significantly high compared to that in a transmission system. The need of improving the overall efficiency of power delivery has forced the power utilities to reduce the losses at distribution level. By minimizing the losses, the system may acquire longer life span and has greater reliability. Therefore after proper installation of voltage regulator losses in the distribution system reduces and hence voltage profile also improved.
Voltage Regulator (VR) or Automatic Voltage Booster (AVB) is essentially an auto transformer consisting of a primary or existing winding connected in parallel with the circuit and a secondary winding with taps connected in series with the circuit. Taps of series winding are connected to an automatic tap changing mechanism.
A voltage regulator is a device that keeps a predetermined voltage in a distribution network despite of the load variations within its rated power [1].In distribution systems operation, shunt capacitor banks and feeder regulators are necessary for providing acceptable voltage profiles to all end-use customers and reducing power losses on large distribution systems [2]. A voltage regulator is equipped with controls and accessories for its tap to be adjusted automatically under load conditions. Moreover, it can be controlled by the installation of devices such as fixed and controlled capacitors banks, transformers with On Load Tap Changers (OLTCs), and Automatic Voltage Regulators (AVRs) [3].

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1.1 Load Flow Solution
In any radial distribution system, the electrical equivalent of a branch 1, which is connected between nodes 1 and 2 having impedance Z1 is shown in Figure. 1[C.L.Wadhwa, „Electrical power systems‟]
Figure.1 Electrical equivalent of a typical branch ‘1’
The voltage at source node is taken as 1.0 p.u. The voltage at node 2 is given by[7]
V2 = V1 – I1 Z1
In general Vn2 = V n1 – Ij Z j -- (1)
where „n1‟ and „n2‟ are sending and receiving ends of branch „j‟ respectively.
By using Eqn. (1), the voltage at any node (except node 1) can be calculated.
The load current at node „i‟ is calculated by
IL i = PL i+j QL i, for i = 2,3, ----,nn -- (2)
Vi
Where,
PL i = Real or Active power load at node i
QL i = Reactive power load at node i
nn= Number of nodes
The real and reactive power losses of branch „j‟ can be calculated as
LP j = Ij2 r j -- (3)
LQ j = Ij2 x j for j=1, 2, ----, nb. -- (4)
where nb= Number of branches
The current in each branch is calculated by applying KCL at node „2‟ shown in Figure 1 the branch current equation obtained is as follows:

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I1= I2 +I5 +I7+IL2 -- (5)
From the above, the current can be calculated in any branch. Initially, a flat voltage profile is assumed at all nodes i.e., 1.0 p.u. Load currents are computed iteratively with the updated voltages at each node.
II. PROBLEM FORMULATION
In a distribution system with an ever increasing load demand there is reduction in voltage and hence power losses increases. Therefore in order to maintain the constant voltage profile and to reduce the power losses, voltage regulators are installed in the distribution system.
2.1 Optimal location of Automatic Voltage Regulators (AVR)
Voltage Regulator (VR) or Automatic Voltage Booster (AVB) is essentially an auto transformer consisting of a primary or existing winding connected in parallel with the circuit and a second winding with taps connected in series with the circuit. In order to maintain the voltage profile and to reduce the power losses these are installed in the distribution systems [6].
• VR provides 10% boost of voltage
• It boosts voltage in four steps of 2.5% each and it also boosts voltage in 32 steps of 0.625% each.
• It has line drop compensation to maintain constant voltage at its location.
The optimal location of voltage regulator (AVR) is defined as function of two objectives, one representing power loss reduction and the other one representing the voltage deviations but both are essential to secure the power supply.
The objective function to be minimized is given below
Minimize f = Σ lossj abc --(6)
Where, P loss jabc is the active power loss in the jth branch after voltage regulator placement.
„nb‟ is the number of branches in the system.
2.2 Tap Position Selection
By finding the optimal number and location of Voltage regulators then tap positions of VR is to be determined as follows.
In general, VR position at node „i‟ can be calculated as [5]
V1i = Vi ± tap× Vrated --(7)
Tap position (tap) can be calculated by comparing voltage obtained before VR installation with the lower and upper limits of voltage
„+‟ for boosting of voltage
„-‟ for bucking of voltage
The node voltages are computed by load flow analysis, described in section 1.1
2.3 Candidate Node Identification using PLI
Power Loss Index (PLI) is power loss based approach to determine the suitable location for placement of voltage regulators. After running the load flows, the total active power loss is given by 281.5877 kW. Therefore Power Loss Index (PLI) are calculated as:

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PLI[j] = (Loss. reduction[j] -Min reduction) --(8)
(Max. reduction - Min. reduction)
2.4 Calculations for Net Savings
The maximum net savings after voltage regulator placement can be calculated is given below [4]
F = Ke× Plr ×8760 ×Lsf – KVR× N(α+β) --(9)
Where,
Plr = Reduction in power losses due to installation of VR
Ke = Cost of energy in Rs./kWh
Lsf= Loss factor = 0.2 Lf + 0.8 Lf2
Lf= Load factor
N = Number of VRs
KVR= Cost of each VR
α= Regulator Setting for resistance compensation
β = Regulator Setting for reactance compensation.
III. IMPLEMENTATION OF PSO
After calculating the total power losses by using load flow analysis and candidate node identification by power loss index, the voltage regulator tap setting at candidate node of the unbalanced radial distribution system is selected using PSO.
3.1 Initialization of PSO Parameters
The control parameters such as lower and upper bounds of node voltage and tap setting of voltage regulators are selected as initialize parameters. Randomly generate an initial swarm (array) of particles with random positions and velocities.
3.2 Evaluation of Fitness Function
The fitness function should be capable of reflecting the objective and directing the search towards optimal solution For each particle or swarm, the voltage regulators are placed at the nodes and run the load flow to calculate the losses and these losses becomes the fitness function of the PSO.
3.3 Optimal Solution
PSO simulates the behaviors of bird flocking. Suppose the following scenario: a group of birds are randomly searching food in an area. There is only one piece of food in the area being searched. All the birds do not know where the food is, But they know how far the food is in each iteration. So what's the best strategy to find the food? The effective one is to follow the bird which is nearest to the food.
PSO learned from the scenario and used it to solve the optimization problems. In PSO, each single solution is a "bird" in the search space. We call it "particle". All of particles have fitness values which are evaluated by the fitness function to be optimized, and have velocities which direct the flying of the particles. The particles fly through the problem space by following the current optimum particles.
PSO is initialized with a group of random particles (solutions) and then searches for optima by updating generations. In every iteration, each particle is updated by following two "best" values. The first one is the best solution (fitness) it has achieved so far. (The fitness value is also stored.) This value is called pbest. Another "best" value that is tracked by the

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particle swarm optimizer is the best value, obtained so far by any particle in the population. This best value is a global best and called gbest.
The modification can be represented by the concept of velocity (modified value for the currentpositions). Velocity of each particle can be modified by the following equation,
Vik+1 =WVik + C1 rand1 × (Pbesti − Xik) + C2 rand2 ×( Gbest – Xik ) --(10)
The rand1, rand2 are the two random numbers with uniform distribution with range of { 0.0 to 1.0 }
W is the inertia weight which shows the effect of previous velocity vector on the new vector.
A larger inertia weight „W‟ facilitates global exploration, while smaller inertia weight „W‟ tends to facilitates local exploration to fine tune. where,
Vik: Velocity of particle i at iteration k,
Vik+1: Modified velocity of particle i at iteration k+1,
W : Inertia weight,
C1, C2 : Acceleration Constants,
rand1, rand2 : Two random numbers
Xik: Current position of particle i at iteration k,
Pbesti : Pbesti of particle i,
Gbest : Gbest of the group.
In the equation (10),
The term rand1 × (Pbesti – Xik ) is called particle memory influence
The term rand 2×(Gbest – Xik) is called swarm influence.
W=Wmax - Wmax- Wmin × iter --(11)
itermax
Where,
Wmax: Initial value of the Inertia weight,
Wmin: Final value of the Inertia weight,
itermax : Maximum iteration number,
iter : current iteration number.
Accordingly, the optimal types and sizes of voltage regulators to be placed at each compensation node can be determined.
3.4 Algorithm for Optimal Location using PLI and Tap setting of VR using PSO
The detailed algorithm is to determine optimal location along with tap setting of voltage regulator is given below.
Step 1: Read system data such as line data and load data of distribution system.

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Step 2: Initialize the PSO parameters such as Number of Agents (M), Number of Particles (N), Number of Iterations (Kmax), Initial value of Inertia weight (Wmax), Final value of Inertia weight (Wmin), Acceleration Constants (C1 & C2).
Step 3: Initialize the parameters as explained in section 5.
Step 4: Obtain the optimal location of VR by using PLI (Power Loss Index) as input.
Step 5: Initialize the swarm by assigning a random position and velocity in the problem hyperspace to each particle, where each particle is a solution of tap setting of VR.
Step 6: Run the load flow and compute the fitness value of each particle using equation (10).
Step 7: Compare the present fitness value of ith particle with its historical best fitness value. If the present value is better than Pbest updating the Pbest, else retain Pbest as same.
Step 8: Find the Gbest value from the obtained Pbest values.
Step 9: Update the particle positions & velocity using eqns. (10) & (11).
Step 10: Apply boundary conditions to the particles
Step 11: Execute steps 6-10 in a loop for maximum number of iterations (Kmax).
Step 12: Stop the execution and display the Gbest values as the final result for optimal tap setting of voltage regulator.
IV. RESULTS AND DISCUSSION
The PSO Parameter values for voltage regulator placement: Number of Particles (N) =10, Number of Iterations (Kmax) =30, Initial value of the inertia weight (Wmax) =0.9 ,Final value of the inertia weight (Wmin) =0.4, Acceleration constants, (C1 & C2)=4. The performance of the proposed algorithm is evaluated for test system of 11kV, 100MVA,33 bus URDS for voltage regulator placement. Proper allocation of VR gives minimum losses and improves voltage profile of the system.The proposed method is illustrated with test system consisting of 33 bus URDS.
4.1 Case Study
Power loss indices for 33 bus URDS is shown in the Figure.2. The proposed algorithm is tested on IEEE 33 bus URDS ans the single line diagram of IEEE 33 bus URDS is shown in Figure.3
Figure 2: Power loss indices for IEEE 33 bus URDS
0510152025303500.10.20.30.40.50.60.70.80.91Branch Number Power loss index

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Line and load data, active and reactive power flows are given in tables 1.Summary of test results of bus IEEE 33 bus URDS for voltage regulator placement are given in table 2. Voltage, Power loss indices, Power loss values before VR placement and Voltage, Power loss values and Tap setting of Voltage regulator of 33-node RDS after VR placement are given in table 3.
From table 2 it is observed that the Active Power loss is reduced from 281.5877 kW to 171.8373 kW i.e, 38.97 % and Reactive Power loss is reduced from 187.9595 kW to 114.0787 kW i.e, 39.30 % .The minimum voltage at node 18 is 0.8819 and after VR placement it is improved by 1.1133. The maximum net saving is Rs. 4383529.7838 after VRs placement. Hence, there is an improvement in the minimum voltage, reduction in active and reactive power losses and maximizing the net savings when compared with before and after voltage regulator placement.
Table. 1: Line data and Load data of IEEE 33 bus Radial Distribution System
Branch
Number
Sending
end bus
Receiving
end bus
Resistance
R (Ω)
Reactance
X (Ω)
Bus
Number
Active Power
PL (kW)
Reactive Power
QL (kVAr)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
0.0922
0.4930
0.3660
0.3811
0.8190
0.1872
0.7114
1.0300
1.0440
0.1966
0.3744
1.4680
0.5416
0.5910
0.7463
1.2890
0.7320
0.0470
0.2511
0.1864
0.1941
0.7070
0.6188
0.2351
0.7400
0.7400
0.0650
0.1238
1.1550
0.7129
0.5260
0.5450
1.7210
0.5740
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
0
100
90
120
60
60
200
200
60
60
45
60
60
120
60
60
60
0
60
40
80
30
20
100
100
20
20
30
35
35
80
10
20
20

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18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
2
19
20
21
3
23
24
6
26
27
28
29
30
31
32
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.1640
1.5042
0.4095
0.7089
0.4512
0.8980
0.8960
0.2030
0.2842
1.0590
0.8042
0.5075
0.9744
0.3105
0.3410
0.1565
1.3554
0.4784
0.9373
0.3083
0.7091
0.7011
0.1034
0.1447
0.9337
0.7006
0.2585
0.9630
0.3619
0.5302
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
90
90
90
90
90
90
420
420
60
60
60
120
200
150
210
60
40
40
40
40
40
50
200
200
25
25
20
70
600
70
100
40
Table.2: Test results of 33-node system before and after VRs placement
Parameters
Before VRs
placement
After VRs placement
(VR at buses 2,5,27)
Reduction in %age
Total Active Power PL (kW)
281.5877
171.8373
38.97 %
Total Reactive Power QL(kVAr)
187.9595
114.0787
39.30 %
Minimum Voltage (p.u)
0.8819
1.1133
-
Voltage regulation
0.4418
0.2341
-
Net saving(Rs.)
-
4383529.7838
-

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Figure.3: IEEE 33- Bus Radial Distribution Network
Table.3: Voltage, Power loss indices, Power loss values before VR placement and Voltage, Power loss values and Tap setting of Voltage regulator of 33-node RDS after VR placement
Branch No.
Bus No.
Before VR Placement
After VR Placement at buses 2, 5,27
Voltage
(p.u)
Active power loss P(kW)
Reactive power loss Q(kVAr)
Power loss index (PLI)
Voltage
(p.u)
Active power
loss P(kW)
Reactive power loss
Q (kVAr)
Bus No. to place VR
Tap setting of Voltage regulator (p.u)
1
2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
10
11
1.0000
0.9960
0.9770
0.9668
0.9568
0.9318
0.9271
0.9205
0.9119
0.9040
0.9028
16.8042
71.3939
27.6696
26.0406
53.2996
2.6787
6.7909
5.8918
5.0230
0.7815
1.2449
8.5661
36.3631
14.0918
13.2629
46.0108
8.8546
2.2442
4.2329
3.5604
0.2584
0.4116
0.2352
1.0000
0.3874
0.3646
0.7465
0.0373
0.0949
0.0823
0.0701
0.0107
0.0172
1.0000
1.0946
1.0793
1.0715
1.1723
1.1533
1.1494
1.1441
1.1373
1.1309
1.1300
11.1904
46.2350
16.3019
15.0653
30.7251
1.7128
4.3250
3.7341
3.1794
0.4942
0.7864
5.7044
23.5489
8.3024
7.6730
26.5234
5.6618
1.4293
2.6827
2.2536
0.1634
0.2600
2
5
15
17

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12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
0.9008
0.8924
0.8893
0.8874
0.8855
0.8828
0.8819
0.9953
0.9906
0.9896
0.9888
0.9722
0.9632
0.9588
0.9291
0.9257
0.9101
0.8989
0.8941
0.8883
0.8871
0.8867
3.7715
1.0322
0.5062
0.3993
0.3571
0.0754
0.2142
1.1081
0.1342
0.0581
4.2998
6.9559
1.7431
3.6496
4.6773
15.8975
11.0276
5.4873
2.2543
0.3017
0.0186
2.9674
1.3586
0.4505
0.2916
0.4768
0.0591
0.2044
0.9985
0.1568
0.0769
2.9380
5.4927
1.3640
1.8590
2.3814
14.0165
9.6070
2.7950
2.2279
0.3516
0.0290
0.0526
0.0142
0.0068
0.0053
0.0047
0.0008
0.0027
0.0153
0.0016
0.0006
0.0600
0.0972
0.0242
0.0509
0.0653
0.2225
0.1542
0.0766
0.0313
0.0040
0
1.1284
1.1217
1.1192
1.1177
1.1162
1.1139
1.1133
1.0939
1.0896
1.0887
1.0880
1.0749
1.0669
1.0628
1.1514
1.2651
1.2540
1.2460
1.2427
1.2385
1.2376
1.2373
2.3793
0.6507
0.3186
0.2512
0.2245
0.0474
0.1770
0.9155
0.1109
0.0480
3.5047
5.6673
1.4191
1.9061
2.4191
8.2091
5.6895
2.8287
1.1567
0.1547
0.0096
1.8720
0.8565
0.2836
0.1834
0.2997
0.0372
0.1689
0.8250
0.1295
0.0635
2.3948
4.4752
1.1104
0.9709
1.2317
7.2378
4.9566
1.4408
1.1432
0.1803
0.0149
27
18
Before voltage regulator placement

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After voltage regulator placement
Voltage comparison before and after VR placement
V. CONCLUSIONS
The proposed PSO based methodology was applied to IEEE 33 bus URDS. The obtained solution has succeeded in
reducing total active power loss 38.97 % in IEEE 33 bus URDS. From the test results, it is concluded that the proposed
model is valid and reliable .The power loss of unbalanced distribution system can be reduced by proper placement of
voltage regulator. In addition to power loss reduction, the voltage profile also improved by the proposed method and then
obtained the maximum net savings.
REFERENCES
[1] D. Rajicic, R. Ackovski, and R. Taleski, “Voltage correction power flow”, IEEE Transactions on Power Delivery,
vol. 9, pp. 1056–1062, Apr. 1994.
[2] M. M. A Salama, N. Manojlovic, V. H. Quintana, and A. Y. Chikhani, “Real-Time Optimal Reactive Power
Control for Distribution Networks”, International Journal of Electrical Power & Energy Systems, vol. 18, no. 3,
pp. 185–193, 1996.

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[3] M. A. S. Masoum, A. Jafarian, M. Ladjevardi, E. F. Fuchs, and W. N Grady, “Fuzzy approach for optimal Placement and sizing of capacitor banks in the presence of harmonic”, IEEE Transactions Power Delivery, vol. 16, no. 2, pp. 822–829, Apr. 2004.
[4] P.V.V. Rama Rao1*, S. Sivanaga Raju , “ Voltage regulator placement in radial distribution system using plant growth simulation algorithm,” International Journal of Engineering, Science and Technology Vol. 2, No. 6, 2010, pp. 207-217
[5] Safigianni and G. Salis, “Optimal voltage regulator placement in radial distribution network,” IEEE Trans. on Power Systems, vol. 15, no. 2, pp. 879–886, May 2000.
[6] H.A Attia, “Optimal voltage profile control and losses minimization of radial distribution feeder” Power System Conference, (MEPCON 2008), pp 453-458, March 2008.
[7] Srikanth Apparaju, Sri Chandan K “impact of Distribution Generation on voltage Levels in Radial Distribution Systems” International Journal of Engineering Research and Applications Vol. 1, Issue 2, pp.277-281, 2010.

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